We now take a closer look at each example [1]}, [2]}, [3]}, [4]} to analyse generic geodesics in the form \( \frac{\rm d~}{\rm d\lambda }(g_{\mu \nu }\dot{x}^{\nu })={{\textstyle \frac{1}{2}}}\partial _{\mu }g_{\nu \rho }\dot{x}^{\nu }\dot{x}^{\rho }\) 
and string propagation in conformal gauge,
\(\!\scalebox {0.8}{\partial _{+}}(g_{\mu \nu }\scalebox {0.8}{\partial _{-}}x^{\nu })+\scalebox {0.8}{\!\partial _{-}}(g_{\mu \nu }\scalebox {0.8}{\partial _{+}}x^{\nu }){+(}H_{\mu \nu \rho }-\partial _{\mu }g_{\nu \rho })\scalebox {0.8}{\partial _{+}}x^{\nu }\scalebox {0.8}{\partial _{-}}x^{\rho }=0\,,\) 
